Coontents

group theory

# Coontents

## Definition

The rank of a Lie group is the dimension of any one of its Cartan subgroups, hence equivalently the dimension of any one of the Cartan subalgebras of its Lie algebra.

For connected compact Lie groups, a Cartan subgroup is a maximal torus, and hence in this case the rank of the Lie group is the dimension of any one of its maximal tori.

## References

Last revised on May 15, 2019 at 10:43:43. See the history of this page for a list of all contributions to it.